I have lived in Nashville for the past 2 years and I am very glad that I stuck with AA after moving here from NYC. They offer more than any other carrier save WN in terms of nonstops (DFW, ORD, LAX, LGA, MIA, STL, DCA) and I have found their fares and schedules to be at least competitive with everyone else.
For the record, DFW, LAX, MIA, and LGA are all mainline (although LGA is switching from 3x mainline to 2x mainline + 2x RJ daily).
Upgrades are incredibly easy, especially on the LGA routes (I never missed an upgrade at the 24 hour mark, even as an AAdvantage Gold).
The Admirals Club is one of the best in the system IMHO and this alone has been enough to make AA my preferred carrier. Last October I was scheduled to fly BNA-ORD-SJC when the club staff called me the night before on my cell phone: "I see you are scheduled to connect through Chicago tomorrow. Your flights are still on-time but we are getting a little concerned for our club members about the weather up there so I made you a duplicate booking through Dallas that will get you in at the same time. Would you like me to cancel the original one?" This kind of pro-active, personal service can be invaluable to a business traveler.
DL may be a better option in the immediate term as they will match your status but I would keep AA in mind long-term, as most people would agree that AAdvantage is a better program and seems more committed to its elite customers.